# KAOPEN Narrative Check

| Model | N | Countries | R² | Z₁ coef | Z₁ SE | Z₁ p | Sig |
|---|---|---|---|---|---|---|---|
| F1: Z₁ × KAOPEN interaction | 3,222 | 99 | 0.029 | -1.2133 | 0.3754 | 0.0012 | *** |
| F2: Closed economies | 1,607 | 75 | 0.025 | -0.9735 | 0.5978 | 0.1036 |  |
| F4: Open economies | 1,615 | 65 | 0.009 | -1.4751 | 0.4281 | 0.0006 | *** |

## Full Coefficients

| Model | Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|---|
| F1: Z₁ × KAOPEN interaction | Z_1 | -1.2133 | 0.3754 | 0.0012 | *** |
| F1: Z₁ × KAOPEN interaction | Z_2 | 0.1580 | 0.0544 | 0.0037 | *** |
| F1: Z₁ × KAOPEN interaction | Z_3 | -0.0059 | 0.0022 | 0.0068 | *** |
| F1: Z₁ × KAOPEN interaction | Z_1_x_kaopen | 0.0051 | 0.0033 | 0.1205 |  |
| F1: Z₁ × KAOPEN interaction | log_gdp_pc | 0.0521 | 0.0149 | 0.0005 | *** |
| F1: Z₁ × KAOPEN interaction | rgdp_growth | -0.0003 | 0.0003 | 0.2763 |  |
| F1: Z₁ × KAOPEN interaction | kaopen | 0.0040 | 0.0058 | 0.4912 |  |
| F1: Z₁ × KAOPEN interaction | nfa_gdp_lag | -0.0005 | 0.0019 | 0.7836 |  |
| F1: Z₁ × KAOPEN interaction | log_gdp_pc | 0.0521 | 0.0149 | 0.0005 | *** |
| F1: Z₁ × KAOPEN interaction | rgdp_growth | -0.0003 | 0.0003 | 0.2763 |  |
| F1: Z₁ × KAOPEN interaction | nfa_gdp_lag | -0.0005 | 0.0019 | 0.7836 |  |
| F2: Closed economies | Z_1 | -0.9735 | 0.5978 | 0.1036 |  |
| F2: Closed economies | Z_2 | 0.1215 | 0.0885 | 0.1700 |  |
| F2: Closed economies | Z_3 | -0.0044 | 0.0036 | 0.2249 |  |
| F2: Closed economies | log_gdp_pc | 0.0333 | 0.0232 | 0.1517 |  |
| F2: Closed economies | rgdp_growth | -0.0003 | 0.0004 | 0.3976 |  |
| F2: Closed economies | nfa_gdp_lag | -0.0008 | 0.0023 | 0.7426 |  |
| F2: Closed economies | log_gdp_pc | 0.0333 | 0.0232 | 0.1517 |  |
| F2: Closed economies | rgdp_growth | -0.0003 | 0.0004 | 0.3976 |  |
| F2: Closed economies | nfa_gdp_lag | -0.0008 | 0.0023 | 0.7426 |  |
| F4: Open economies | Z_1 | -1.4751 | 0.4281 | 0.0006 | *** |
| F4: Open economies | Z_2 | 0.1902 | 0.0606 | 0.0017 | *** |
| F4: Open economies | Z_3 | -0.0070 | 0.0024 | 0.0031 | *** |
| F4: Open economies | log_gdp_pc | 0.0977 | 0.0173 | 0.0000 | *** |
| F4: Open economies | rgdp_growth | -0.0005 | 0.0003 | 0.1423 |  |
| F4: Open economies | nfa_gdp_lag | 0.0113 | 0.0080 | 0.1588 |  |
| F4: Open economies | log_gdp_pc | 0.0977 | 0.0173 | 0.0000 | *** |
| F4: Open economies | rgdp_growth | -0.0005 | 0.0003 | 0.1423 |  |
| F4: Open economies | nfa_gdp_lag | 0.0113 | 0.0080 | 0.1588 |  |

*Interaction Z₁×KAOPEN = 0.0051 (p=0.1205): positive → openness attenuates the demographic depreciation effect.*

*KAOPEN tercile cutoffs: -1.254, 2.281*